You play the following game against a devilishly clever opponent. On the table, there are
two bowls filled with glass beads. In each move, depending on whose turn it is, you or your
opponent can do one of the following.
� Move one bead from the first bowl to the second bowl.
� Remove one bead from the second bowl.
At any point in the game, let x denote the number of beads in the first bowl and y denote
the number of beads in the second bowl. If x+ y is even, it is your turn to move. If x+ y is
odd, it is your opponent�s turn to move.
At each position of the game, you get some points that depend on the number of beads,
x and y, in the two bowls. This is given by a function f(x, y) = Ax2 +By2 +Cxy, where A,
B and C are integers that are fixed each time the game is played.
The game starts with M beads in the first bowl and N beads in the second bowl. As the
game progresses, beads are removed. The game ends when both bowls are empty.
Your score for the game is the sum of the values f(x, y) for each position (x, y) that the
game passes through, starting from (M,N) and ending with (0, 0). Your aim is to obtain
as high a score as possible, no matter what moves your opponent chooses. Remember that
your opponent is fiendishly ingenious and will always play in such a way as to minimize your
score.
For example, suppose the game starts with 2 beads in each bowl and the score function
is f(x, y) = x2 − y2 − xy: that is, A = 1, B = −1 and C = −1. Here are some plays of
the game�the positions where you choose the move are enclosed in boxes and the positions
where your opponent moves are not enclosed in boxes.
� (2,2) ! (2,1) ! (2,0) ! (1,1) ! (1,0) ! (0,1) ! (0,0).
For this sequence of moves, your total score is f(2, 2) + f(2, 1) + f(2, 0) + f(1, 1) +
f(1, 0) + f(0, 1) + f(0, 0) = (−4) + 1 + 4 + (−1) + 1 + (−1) + 0 = 0.
� (2,2) ! (1,3) ! (0,4) ! (0,3) ! (0,2) ! (0,1) ! (0,0)
For this sequence of moves, your total score is f(2, 2) + f(1, 3) + f(0, 4) + f(0, 3) +
f(0, 2) + f(0, 1) + f(0, 0) = (−4) + (−11) + (−16) + (−9) + (−4) + (−1) + 0 = −45.
In this particular game, the best possible score that you can achieve if you consider all
possible moves that your opponent can choose is −22. Recall that your devilishly clever
opponent always plays in such a way that your score is minimized.
Input format
The input consists of a single line containing five integers, M, N, A, B and C where M and
N are the number of beads initially in the first and second bowl, respectively and A, B and
C are the coefficients of the score function f(x, y) = Ax2 + By2 + Cxy.
3
Output format
The output should be a single integer, the maximum score that you can achieve in this game.
Test data
In all inputs, 1  M,N  600 and −1000  A,B,C  1000.
Example
Sample input
2 2 1 -1 -1
Sample output
-22